A Course in the Theory of Groups

A Course in the Theory of Groups is a comprehensive introduction to the theory of groups - finite and infinite, commutative and non-commutative. Presupposing only a basic knowledge of modern algebra, it introduces the reader to the different branches of group theory and to its principal accomplishments. While stressing the unity of group theory, the book also draws attention to connections with other areas of algebra such as ring theory and homological algebra.
This new edition has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included. There are three main additions to the book. In the chapter on group extensions an exposition of Schreier's concrete approach via factor sets is given before the introduction of covering groups. This seems to be desirable on pedagogical grounds. Then S. Thomas's elegant proof of the automorphism tower theorem is included in the section on complete groups. Finally an elementary counterexample to the Burnside problem due to N. D. Gupta has been added in the chapter on finiteness properties.

1 Fundamental Concepts of Group Theory. - 2 Free Groups and Presentations. - 3 Decompositions of a Group. - 4 Abelian Groups. - 5 Soluble and Nilpotent Groups. - 6 Free Groups and Free Products. - 7 Finite Permutation Groups. - 8 Representations of Groups. - 9 Finite Soluble Groups. - 10 The Transfer and Its Applications. - 11 The Theory of Group Extensions. - 12 Generalizations of Nilpotent and Soluble Groups. - 13 Subnormal Subgroups. - 14 Finiteness Properties. - 15 Infinite Soluble Groups.